Properties of the Proximate Parameter Tuning Regularization Algorithm

Abstract

An important aspect of systems biology research is the so-called "reverse engineering" of cellular metabolic dynamics from measured input-output data. This allows researchers to estimate and validate both the pathway's structure as well as the kinetic constants. In this paper, the recently published 'Proximate Parameter Tuning' (PPT) method for the identification of biochemical networks is analysed. In particular, it is shown that the described PPT algorithm is essentially equivalent to a sequential linear programming implementation of a constrained optimization problem. The corresponding objective function consists of two parts, the first emphasises the data fitting where a residual 1-norm is used, and the second emphasises the proximity of the calculated parameters to the specified nominal values, using an infinity-norm. The optimality properties of PPT algorithm solution as well as its geometric interpretation are analyzed. The concept of optimal parameter locus is applied for the exploration of the entire family of optimal solutions. An efficient implementation of the parameter locus is also developed. Parallels are drawn with 1-norm parameter deviation regularization which attempt to fit the data with a minimal number of parameters. Finally, a small example is used to illustrate all of these properties.

An empirical modeling platform to evaluate the relative control discrete CHO cell synthetic processes exert over recombinant monoclonal antibody production process titer

“…1; Supplementary Material 1). For each model un‐measured parameters were fitted to the empirical data using 100 statistical best‐fit parameter sets which were calculated using the PPT algorithm (Brown et al, 2010; Dimelow and Wilkinson, 2009; O'Callaghan et al, 2010; Wilkinson et al, 2008). A successful fit was defined to have a sum of squared residuals <0.5, where the residual is the absolute difference between the empirically derived data point and the model‐predicted value in logarithmic space.…”

“…The model was built and solved using Sentero, an in‐house biochemical modeling software tool which uses Matlab's ODE solver to provide a computationally efficient simulation engine (O'Callaghan et al, 2010; Wilkinson et al, 2008). Unmeasured parameters were fitted to the experimental data using the proximate parameter tuning (PPT) algorithm to yield “best‐fit” model parameters for each day of analysis during culture as described in detail previously (Brown et al, 2010; Dimelow and Wilkinson, 2009; O'Callaghan et al, 2010; Wilkinson et al, 2008). The same parameter ranges were sampled for each model fit (Supplementary Material 2).…”

Towards a unifying, systems biology understanding of large-scale cellular death and destruction caused by poorly liganded iron: Parkinson’s, Huntington’s, Alzheimer’s, prions, bactericides, chemical toxicology and others as examples

“…While phlebotomy is a very traditional nostrum, often assumed or considered to have rather dubious or at best modest scientific support, there is in fact increasing literature implying its benefits in a variety of conditions (e.g. Aigner et al 2008; Beutler 2007; Broedbaek et al 2009; Brudevold et al 2008; Busca et al 2010; DePalma et al 2007, 2010; Dereure et al 2008; Desai et al 2008; Dwyer et al 2009; Equitani et al 2008; Facchini et al 2002; Fargion et al 2002; Fernández-Real et al 2002; Fujita et al 2009; Fujita and Takei 2007; Hayashi et al 2006; Hayashi and Yano 2002; Heathcote 2004; Horwitz and Rosenthal 1999; Hua et al 2001; Kaito 2007; Kaito et al 2006; Kato et al 2001, 2007; Kom et al 2006; Rajpathak et al 2009; Sullivan 2009; Sumida et al 2009; Tanaka et al 2007, 2009; Toyokuni 2009b; Zacharski et al 2008). Plausibly such benefits are due to its role in decreasing iron stores.…”

Cell line‐specific control of recombinant monoclonal antibody production by CHO cells

“…Model parameters were fitted to the experimental data generated for each cell line (see below) using the proximate parameter tuning (PPT) algorithm (Brown et al, 2010;Dimelow and Wilkinson, 2009;Wilkinson et al, 2008). In common with most other parameter estimation techniques, this method uses an iterative approach in which parameter values are adjusted in order to match the model outputs to the measured data.…”

“…This analysis produced a cell line-specific set of calculated model parameter values representing the statistical best fit (Brown et al, 2010) to the biological data (Table III). For each cell line, no variance in the PPT derived parameters were observed, even where a large area of the parameter space was sampled.…”